A) \[\frac{1}{64}\]
B) \[\frac{1}{32}\]
C) \[\frac{1}{16}\]
D) \[\frac{1}{4}\]
Correct Answer: A
Solution :
Given : Radius of the first sphere \[{{R}_{1}}=R\] Radius of the second sphere \[{{R}_{2}}=4R\] The heat capacity is given by as \[\Delta Q=\frac{4}{3}\pi {{r}^{3}}\rho \,c\propto {{R}^{3}}\] Hence,\[\left( \frac{\Delta {{Q}_{1}}}{\Delta {{Q}_{2}}} \right)=\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)={{\left( \frac{1}{4} \right)}^{3}}=\frac{1}{64}\]
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